CHAPTER II OPERATING PROCEDURE AND REVIEW OF SAMPLING PLANS

Transcription

1 CHAPTER II OPERATING PROCEDURE AND REVIEW OF SAMPLING PLANS This chapter comprises of the operating procedure of various sampling plans and a detailed Review of the Literature relating to the construction and selection of various sampling plans indexed through various parameters. Section 2.1: Operating procedure and Review of Single Sampling plan Section 2.2: Operating procedure and Review of Double Sampling Plan Section 2.3: Operating procedure and Review of Conditional Double Sampling Plan Section 2.4: Operating procedure and Review of Double Sampling Plan of the type DSP- (0,1) Section 2.5: Operating procedure and Review of Chain Sampling Plan of the type ChSP- 1 Section 2.6: Operating procedure and Review of Chain Sampling Plan of the type ChSP- 2 Section 2.7: Operating procedure and Review of Chain Sampling Plan of the type ChSP- (0,1) Section 2.8: Operating procedure and Review of Tightened- Normal- Tightened Plan of the type TNT- (ni.n2:0) Section 2.9: Operating procedure and Review of Tightened- Normal- Tightened Plan of the type TNT- (n;ci,c2) Section 2.10: Operating procedure and Review of Repetitive Group Sampling Plan Section 2.11: Operating procedure and Review of Conditional Repetitive Group Sampling Plan Section 2.12: Operating procedure and Review of Link Sampling Plan Section 2.13: Operating procedure and Review of Reliability based mixed sampling plan. Section 2.14: Designing of Reliability based mixed sampling plan. Section 2.15: Summary. 16

2 2.1 OPERATING PROCEDURE AND REVIEW OF SINGLE SAMPLING PLAN In single sampling plan by attributes, the lot acceptance procedure is characterized by two parameters n and c. The operating procedure for a single sampling plan is given as follows: 1. Select a random sample size V from a lot of size N* 2. Inspect all the articles included in the sample. Let'd' be the number of defectives in the sample. 3. If d < c, accept the lot. 4. If d > c, reject the lot. The operating characteristic of single sampling plan is given by PAp) = f- -":P ("ipy r=0 r! Peach and Littauer (1946) have given tables for determining the single sampling plai for fixed a = P = Burguess (1948) has given a graphical method to obtain single sampling plans for the given (pt. 1- a) and (p2. p). Grubbs (1949) has given a table, which can be used for selecting a single sampling at AQL and LQL. Cameron (1952) has also given a table which is an extension of Peach and Littauer (1946) Guenther (1969) has developed a systematic search procedure for finding a single sampling plan for the given pi, p2, a and P based on Binomial. Hyper geometric and Poisson models. Golub (1953) has given a method and tables for finding the acceptance number c of a single sampling plan involving minimum sum of producer and consumer risks when the sample size n is fixed. Dodge and Roming (1959) have considered double sampling plans as an extension of single sampling plan. A detailed comparison of various attributes sampling plans and the merits of the double sampling plan can be seen in Duncan (1986) and Schilling (1982). Soundararjan (1975) used the MAPD in a lot as the standard quality and the tangent intercept of the OC curve at the inflection point to the p-axis, which ensures 17

3 sharpness of the OC curve.he proposed a selection procedure for single sampling plan indexed with MAPD (p*) and K= pt/p* where pt is the intercept of the tangent from the point of inflection to the OC curve. Soundararajan and Govindaraju (1983 a) have made contributions in designing single sampling plans. Latha (1988) has constructed tables for mixed sampling plans having single sampling as an attribute plan indexed through AQL and LQL. Devabharathi (1990) has designed mixed sampling plans having single sampling plan as an attribute plan indexed through AQL and IQL. Radhakrishnan (2002) contributed to the study on the selection of certain Acceptance sampling plans indexed through MAAOQ. Sampathkumar (2008) constructed mixed Variables-Attributes sampling plans. Sekkizhar (2008) designed sampling plans using intervened random effect Poisson distribution. Radhakrishnan and Ravishankar (2008) constructed SSP for three attribute classes indexed through AQL. Radhakrishnan and Mohanapriya (2008) studied single sampling plan using Conditional weighted Poisson Distribution. Radhakrishnan and Sivakumaran (2008) constructed and selected six sigma sampling plan indexed through six sigma quality level 2.2 OPERATING PROCEDURE AND REVIEW OF DOUBLE SAMPLING PLAN In double sampling plan by attributes the lot acceptance procedure is characterized by the parameters N. n, n2. Ci and c2.the operating procedure for a double sampling plan is given as follows: 1. Select a random sample of size ni' from a lot of size N 2. Inspect all the articles included in the sample. Let d' be the number of defectives in the sample. 3. If di < C, accept the lot 4. If di > C2, reject the lot. 5. If C +1< dj < c2, take a second sample of size n2' from the remaining lot and find the number of defectives d2 > 6. If dt + d2< c2,accept the lot. 7. Ifd + d2 >c2,reject the lot 18

4 Un^er Poisson model, the OC function of the double sampling plan is given by: '(n<p)' r\ + * = f,+l p)' k! i r! The performance measures of double sampling plan can be seen in Schilling (1982).There are number of tables available to design a double sampling plan including Dodge and Roming (1959) which provide Double sampling plans with minimum Average Total Inspection. Duncan (1986) has provided a compilation of Poisson Unity and operating ratio p2 /pi values for the Double sampling plans taken from the tables of US Army Chemical Corps Engineering Agency (1953). Hald (1981) has constructed tables for single and double sampling plans with the fixed 5% procedures and 10% consumer's risks. Guenther (1970) developed a trial and error procedure for finding double sampling plans for given (pi,l-«)and (p2,p). Schilling and Johnson (1980) have developed a table for the construction and evaluation of matched sets of single, double and multiple sampling plans. Muthuraj (1988) constructed tables based on the Poisson distribution for selecting a double sampling plan for a given (p0, ho ) or (p*, h*). Similarly, Soundararajan and Vijayaraghavan (1989 a) have given tables for selecting double sampling plan for given AQL and AOQL based on equal rejection numbers. Further.Soundararajan and Arumainayagam( 1990) provided tables for easy selection of double sampling plan indexed by AQL, AOQL and LQL. Devaarul (2003) constructed tables for mixed sampling plans having double sampling plan as an attribute plan indexed through AQL and IQL. 2.3 OPERATING PROCEDURE AND REVIEW OF CONDITIONAL DOUBLE SAMPLING PLAN In Conditional double sampling plan by attributes the lot acceptance procedure is characterizes by the parameters N, ni, n2, C, c2 and C3 The operating procedure for a conditional double sampling plan is given below: 19

5 1. Select a random sample siz^ V(=ni = n2) from a lot of size "N 2. Inspect all the articles included in the sample. Let df be the number of defectives in the sample If d] < Ci, accept the lot If d > c3, reject the lot. 5. If Ci +1< di < C3, take a second sample of size n2' from the remaining lot and find the number of defectives d2 * 6. If d2 < c2 or dt + d2 < C3 accept the lot otherwise reject the lot. given by: Under Poisson model the OC function of the Conditional double sampling plan is Vijayaraghavan (1990) has provided procedures and tables for the selection of conditional double sampling plans with various entry parameters. A search procedure is developed to determine the parameters of the plans when two points on the OC curve are specified. Baker and Brobst (1978) proposed conditional sampling procedures which are similar in structure to double sampling. These conditional double sampling procedures have operating characteristic (OC) curves identical to those of comparable double sampling procedures. Conditional double sampling is operationally different from double sampling in that the results of the second sample, if required, are obtained from a related lot and not from the current lot. According to Baker and Brobst (1978), using sample information from related lots results in more attractive OC curves and smaller sample sizes. This reduction in sample size is the principal advantage of these procedures over traditional sampling procedures. 2.4 OPERATING PROCEDURE AND REVIEW OF DSP-(0,1) In DSP-(0,1) plan by attributes the lot acceptance procedure is characterized by the parameters N, ni, n2, ci = 0, c2 =l.the operating procedure for DSP (0,1) plan is given as follows: 20

6 1. Select a random sample size nj from a lot of size "N' 2. Inspect all the articles included in the sample. Let 'dl be the number of defectives in the sample. 3. If di=0, accept the lot 4. If di > 1, reject the lot. 5. If d = 1, take a second sample of size n2? from the remaining lot and find the number of defectives 'd If d2 = 0, accept the lot. 7. If d2>l, reject the lot. Under Poisson model, the OC function of the DSP-(0,1) plan is given by : Pa(p) = e -np + np e _np <i+1) Where n = ni and n2 = (ni)(i), (i>0) Vijayaraghavan (1990) mentioned the situations for which DSP-(0,l)plan can be used and presented tables for selection of DSP-(0,1) plan under Poisson and Binomial conditions. Search procedure was also used to select the plan parameters. Although DSP-(0,1) plan is valid under general conditions for applications of attributes sampling inspection, the plan will specially be useful to product characteristics involving costly or destructive testing. 21

7 2.5 OPERATING PROCEDURE AND REVIEW OF CHAIN SAMPLING PL4N OF THE TYPE ChSP-1 The operating procedure for ChSP-1 is as follows: 1. Select a random sample of size n from a lot of size N! 2. Inspect all the articles included in the sample. Let "d be the number of defectives in the sample. 3. If d = 0, accept the lot. 4. If d > 2, reject the lot. 5. Accept the lot if d-1 and if no defective units are found in the immediately proceeding M' samples of size n\ Thus a ChSP-1 plan has two parameters namely n, the sample size for each submitted lot and i, the number of previous samples on which the decision of acceptance or rejection of the lot is based. Dodge s (1955) has given OC curves of ChSP-1 plans with various values for n=4,5,6 & 10 and M,2,3,4,5 & co. Under the assumptions of Poisson model the OC function of ChSP-1 plan is given as: Pa(p)= e-t+npie-ty" When i = co, the OC function of a ChSP-1 plan reduces to the OC function of single sampling plan with c=0. Similarly when i=0, the OC function of a ChSP-1 plan reduces to the OC function of single sampling plan with c=l. Clark (1960) has given a procedure for the selection of ChSP-1 plan given po.95 and po-io. Fred Frishman (1960) developed two types of chain sampling plans (ChSP-4 and ChSP-4A), which are extension of ChSP-1 plan in which rejection number greater than 1 is included. Soundararajan (1971, 1978a, 1978b) has constructed tables for selection o ChSP-1 plan. Soundararajan and Govindaraju have made contributions in designing ChSP-1 plans. Soundararajan and Doraiswamy (1984) have constructed Chain Sampling Plans (ChSP-1) indexed by inflection point and Point of Control. Devaarul (2003) has made contributions to mixed sampling plans with ChSP-1 plan as attribute plan. 22

8 2.6 OPERATING PROCEDURE AND REVIEW OF CHAIN SAMPLING PLAN OF THE TYPE ChSP-2 Shankar et.al. (1991) developed a new chain sampling plan of the type ChSP-2 in which a lot even with two defects in its sample can still be accepted if last defect found was far enough back in the history of products. The OC functions of the plan have been derived by GERT (Graphical Evaluation and Review Technique) approach. by Under the assumption of Possion model, the OC function of ChSP-2 plan is given pp> Pt(P) = P0 + P2%+-UL (i) \ (n D')2e~"lP where P^ =e ":P,Pl = n2pe ":PandP The operating procedure for ChSP-2 is given as follows: 1. Select a random sample of size *n' from a lot of size N' and count the number of defectives in the sample. 2. Accept the lot if. (a) No defectives are found in the sample. (b) One or two defectives are found in the sample but no defectives were found in the previous T samples 3. Reject the lot. otherwise. 2.7 OPERATING PROCEDURE AND REVIEW OF CHAIN SAMPLING PLAN OF THE TYPE ChSP (0,1) A chain sampling plan ChSP (0,1), which is the extension of ChSP-4 plans, was extensively studied by Stephens and Dodge in various technical reports and papers. A ChSP(0,l) with different sample sizes in the two stages can be represented as ChSP (ni, n2,ki,k2.c,c2). The operating procedure for the ChSP (0,1) is as follows: 1. Select a random sample of size nt, units from the first lot, and in general nm from succeeding lots when operating in the mth stage of the criteria, (m=l,2). 23

9 2. Record the number of defectives d, in each sample and sum the number of defectives D, in all samples from the first up to and including the current sample. 3. Accept the lot associated with each new sample during the cumulation as long as Di < C) ; 1 < i < k, 4. When ki consecutive samples have all resulted in acceptance, continue to sum the number of defectives, D, in the k] samples plus additional samples up to not more than k2 samples. 5. Accept the lot associated with each new sample during the cumulation as long as Di < c2; k < i < k2 6. When the second stage has been successfully completed, start cumulation of defectives as a moving total over k2 samples by adding the current sample result while dropping from the sum, the sample result of the k2th proceeding sample. Continue this procedure as long as Di < c2;(i > k2) and in each instance accept the lot. 7. If for any sample at any stage of the above procedure, as Dj> cm. reject the corresponding lot and return to step 1 and a fresh restart of the cumulation procedure is started. Dodge and Stephens (1964) have studied generalized ChSP-1 plan as a two-stage ChSP-(0,l) plan with n = ni = n2. The OC function of ChSP-(0,l) plan is given as PJP) = />0(l-/>) + f>^(1-/^),, Where P0 = Pi = ki = k2 = Probability for getting exactly zero nonconformities in a sample of size n2 Probability of getting exactly one nonconformity in a sample of size n2 Minimum number of successive samples required to be free from nonconformities before cumalation can take place. Maximum number of successive samples over which the cumalation of nonconformities take place. It can be noted that whenever ki = k2-1 = i, the Probability of acceptance of ChSP- (0,1) plan will reduce to the Probability of acceptance of ChSP-1 plan. 24

10 Stephens and Dodge (1964) have described ChSP-( Ci. c 2) plans with Ci=0. c 2=2 and c,=l and c2=2. Stephens and Dodge (1966) have discussed Chain-Sampling plans ChSP-(0,3) and ChSP-(l,3). Soundararajan and Govindaraju (1983b) have constructed Chain Sampling plan ChSP-(0,l). Radhakrishnan (2002) has constructed tables for Continuous sampling plans indexed through MAAOQ amd AOQL with ChSP-(0,l) plan as attribute plan. 2.8 OPERATING PROCEDURE AND REVIEW OF TIGHTENED - NORMAL - TIGHTENED PLAN OF THE TYPE TNT (n,,n2 ;0). The operating procedure of TNT (ni,n2 ;0) plan is as follows: 1. Inspect using Tightened inspection with the sample size ni and c=0. 2. Switch to Normal inspection when t' lots are accepted under Tightened inspection. 3. Inspect using Normal inspection with sample size n2 (< ni) and c=0. 4. switch to tightened inspection (after a rejection) if an additional lot is rejected in the next s' lots. The OC function for TNT (ni,n2 ;0) plan is given by Pin) ^(1~^)(1-/?i)( -/?2) + fta( -/?l)(2-j>2){1) (1 -p2')(i -pdo -Pl) + pl(\- px)(2 - p\) Where pi = probability of acceptance under tightened inspection = e'v p2 = probability of acceptance under normal inspection = e n2p A single defective unit of the sample, in a compliance testing, calls for rejection of the entire lot. To overcome this undesirability, Tightened- Normal- Tightened Plan (TNT) was developed by Calvin (1977), Suresh and Balamurali (1994) and Romboski (1969) introduced a new entry parameter called Cross over point (COP) which is the point at which both the Tightened and Normal inspection plan in a system make an equal contribution to the composite OC function. Balamurali (2001) has developed TNT (ni,n2 ;0) and TNT (n;0,l) using COP. 25

11 2.9 OPERATING PROCEDURE AND REVIEW OF TIGHTENED- NORMAL- TIGHTENED PLAN OF THE TYPE TNT- (n;c,,c2) The operating procedure of TNT (n;c].c2) plan is as follows: 1. Inspect using Tightened inspection with the sample size n and acceptance number C =0. 2. Switch to Normal inspection when'f lots are accepted under Tightened inspection. 3. Inspect using Normal inspection with sample size n and acceptance number C2= Switch to Tightened inspection after a rejection if an additional lot is rejected in the next s lots. The OC function for TNT (n;cj,c2) plan is given by P,p).. Pi0 - pix1 - p\x* - p2)+piplo ~ Pi X2 - p 2)(]) AP) (1 ~ Pi )(1 - Pi )(1 ~P2) + P) (1 T7})(2 p'l) Under the condition of the application of the Poisson model, when ci =0, the probability of acceptance under tightened inspection becomes Pi = e'np when ci =1, the probability of acceptance under normal inspection becomes p2 =( 1 +np) e'np The above-mentioned shortcoming can be overcome to some extent if one follows the Tightened Normal Tightened (TNT) sampling scheme devised by Calvin (1977). This scheme utilizes c=0 sampling plans of different sample sizes, together with switching rules, to build up the shoulder of the OC curve. This TNT scheme was designated as TNT-(ni,n2;0). Vijayaraghavan (1990) developed another type of TNT scheme designated as TNT - (n;ci,c2). This is also a scheme involving switching between two sampling plans. When the product is forthcoming in a stream of lots and given acceptance numbers are maintained, the TNT - (n; ci, c2) scheme is particularly appropriate. This scheme utilizes the single sampling normal plan with a sample size n and acceptance number c2, as well as the single sampling tightened plan with a sample size n and acceptance number ci (< 26

12 c2). The sampling plans (n, C ) and (n,c2), together with the switching rules, build up the shoulder of the OC curve in a manner similar to that of the switching rules of M1L-STD- 105D (1963). Suresh and Balamurali (1991) studied the TNT (n;0.l) scheme indexed through various parameters such as AQL,AOQL,IQL and LQL OPERATING PROCEDURE AND REVIEW OF REPETITIVE GROUP SAMPLING PLAN 1. Select a random sample of size n from a lot of size N" 2. Inspect all the articles included in the sample. Let d' be the number of defectives in sample. 3. (i) If d < C, accept the lot. (ii) If d > c2, reject the lot (iii) If C < d< c2, repeat the steps 1,2 and 3. Under the assumption of Poisson model, the OC function of RGS plan is given by Pa(p) Zj 1 < =0 ' Sherman (1965) has introduced repetitive group sampling plan in which a sample is drawn and the number of defectives is counted. According to a fixed criterion, the lot is either accepted, rejected or the sample is completely disregarded and one has to begin wi#i a new sample in order to sentence a lot. This is continued until the fixed criterion indicates us to either accept or reject the lot. Govindaraju (1987) has shown that the OC functions of Sherman (1965), Romboski (1969) and Wortham and Mogg (1970) are essentially the same. Subramani (1991) has developed Repetitive Group Sampling plan involving minimum sum of risks. Kuralmani (1992) has designed Repetitive Group Sampling plan and certain related conditional sampling plans for obtaining the minimum sample size. Soundarajan and Ramasamy (1984, 1986) have made contributions to RGS plans. Suresh (1993) has also studied the RGS plan indexed through PQL (Producer s Quality Level) and CQL 27

13 (Consumer's Quality Level) by considering filter and incentive effects. Quick Switching System with RGS as reference plan has developed by Devaraj Arumainayagam (1991). Devaaarul (2003) has developed mixed sampling plans with RGS plan as attribute plan OPERATING PROCEDURE AND REVIEW OF CONDITIONAL RGS PLAN The operating procedure of conditional RGS plan is given as follows: 1. Select a random sample of size n' from a lot of size W 2. Inspect all the articles included in the sample. Let d' be the number of defectives in the sample. 3. If d < ci, accept the lot. 4. If d > c2. reject the lot. 5. Ifc, < d < c2 utilize the information of the next preceding T successive lots (i.e..) the current lot is accepted if the preceding "r successive lots result shows d < C in the sample, otherwise reject the lot. Under the assumption of Poisson model, the OC function of conditional RGS (CRGS) plan is given by Pa(p) = Radhakrishnan (2002) has constructed tables for continuous sampling plans indexed through MAAOQ and AOQL with conditional RGS plan as attribute plan. Conditional sampling plans come under special purpose plans. Sampling plans may be classified under cumulative and non-cumulative type. Under non-cumulative sampling plans, current sample results alone are used for arrival of a decision whether to accept or reject a lot. In the cumulative types of sampling plans, both current and past sample results are used for making such decision. Link sampling plan (LSP) comes under conditional sampling plans, which is classified as cumulative type of sampling plan. The conditional sampling has been developed to reduce the sample size and the inspection cost of the decision process using sample results from the past lots does not reveal the 28

14 exact situation. Hence, this led to the development of fixed deferred state sampling procedures by the Worth am and Baker (1971).These sampling plans utilize sample result from future in order to sentence the current lot OPERATING PROCEDURE AND REVIEW OF LINK SAMPLING PLAN The operating procedure of link sampling plan is as follows: 1. From lot T select a random sample of size ni! and find the number of defectives 'd, in the sample. 2. If the number of defectives d, <cj, accept the lot. 3. If the number of defectives d; >c3, reject the lot. 4. If c,<d,<c3, combine the total number of defectives from the immediate past and future lots, Dj= dj-t + d; + dj+i 5. 5.If D, < c2, accept the lot i ; and reject the lot if D, >C3 The operating procedure is identical to the usual double sampling plan with second sample sizes being twice that of the first sample. But in link sampling plan when the decision is postponed, the sample results from the neighboring lots are used for making a unique decision. Under the assumption of Poisson model, the OC function of LSP plan is given by W-,-1 pap) = 'EPti+Pc^ Z r/=0 Vn+Pc.2 X n= ^2Z^ where, q np(wdy1 Pr =-----0,1,2...c2 ri\ and e~k"p(knpy' -,rt =0,1,2...c3-(c, +1) n\ Harishchandra and Srivenkataramana (1982) have developed link sampling plans. In this scheme whenever a second sample is required, the sample results of the neighboring lots,(past & future) are utilized. The operating characteristics function of link sampling plan is identical with that of double sampling plan. Hence link-sampling plan 29

15 can be proposed as an alternative to double sampling situation. Harishchandran and Srivenkataramana (1982) have also developed partial link sampling plans, moreover, in link sampling plan,the average sample number is V where as in double sampling plan,the average number is more than n' if the lot requires a second sample for making a unique decision. 2.13: OPERATING PROCEDURE AND REVIEW OF RELIABILITY BASED MIXED SAMPLING PLAN. The operating procedure of Reliability based mixed sampling plans (RMSPs) is as follows: 1. Determine the four parameters nj. n2. k" and c with reference to OC curve. 2. Take a random sample of size nj from the lot assumed to be large and put them into life test till time t0 under given environmental conditions. 3. Let m be the total number of specimens that failed during the life test. Let x,.nl, x>n,... xm,m denote the progressively censored life times of a random sample of ni test specimens in the first stage. 4. If the sample order statistic // = x n > A = L + K <x then accept the process or lot. 5. If the sample order statistic ju = x,, < A = L + K a then take another sample of size n2 from the same lot and put them into life test. Call it as second stage. 6. Count the number of specimens (d) that failed to confirm the specification limit L till L,. the test duration. 7. If the number of non-conformities d < c, accept the process otherwise reject it. 8. Replace all the non-conformities with conformities. Schilling (1982) studied acceptance sampling in quality control, Radhakrishnan (2002) made contribution to the study on selection of certain acceptance sampling plans. Devaarul (2003) and Sampath Kumar (2008) studied variables - attributes mixed sampling plan and explained their advantages over variable and attribute sampling plans. The concept of Reliability was also applied in the construction of sampling plans. Latha (1988) and Devabharathi (1990) studied mixed acceptance sampling plans. Oliver and Springer (1972) and Latha (2002) studied Bayesian attribute acceptance plans. The 30

16 Reliability concept is more important in life testing procedure and is very much applied in all major industries of developing and developed countries. A sampling plan involving ReSability concepts is much more essential. 2.14: DESIGNING OF RELIABILITY BASED MIXED SAMPLING PLAN. The Reliability based mixed sampling plans have been designed under two cases of significant interest. In the first case sample size ni is fixed and a point on the OC curve is given. In the second case plans are designed when two points on the OC curve are given. The procedure for designing the Reliability based mixed sampling plans to satisfy the above-mentioned conditions was provided by Schilling (1967). Using Schilling's procedure, Latha (1988) has designed and matched the mixed plans. Devabharathi (1990) has designed mixed plans indexed through AQL and IQL and Devaarul (2003) has made contributions to Reliability based mixed sampling plans. This section deals with the procedure for designing the Reliability based mixed sampling plans. The procedures used in this thesis are discussed in the sections at the end, the contributions are made by the author are given in detail. The procedure for the construction of Reliability based mixed sampling plans is provided by Schilling (1967) for a given nf and a point on the OC curve. A modified procedure for the construction of Reliability based mixed sampling plans for a given MAPD and ny is given below. a. Assume that the mixed plan is independent. b. Decide the sample size n( (for variable sampling plan) to be used. c. Calculate the acceptance limit for the variable sampling plan as A = L + k er k = -1 +[(l-p*)m/(l-po] 1/(m'!) d. Split the probability of acceptance P* as P* and P* such that p* = p* + (1- p*) p* where P* is the probability of acceptance assigned to the Reliability based variable sampling plan and p* is the probability of acceptance assigned to the attribute sampling plan. Fix the value of p». e. Determine P* as P* = (P* - P*)/ (1- p*) f. Determine the appropriate second stage sample of size n2 and T from Pa(p) = p* for p = p* 31

17 Using the above procedure tables can be constructed to facilitate easy selection of Reliability based mixed sampling plan with any attribute plan indexed through MAPD and the quality 'p,'. The author has used the procedures Reliability based mixed sampling plan (Independent case) using MAPD, AQL, IQL. LQL and MAAOQ. In the second stage of Reliability based mixed sampling plans author has used Poisson distribution for the construction of plans. Using Schilling's (1967) procedure, the Reliability based mixed sampling plans are constructed by the author using Single sampling plan, Double sampling plan. Conditional Double sampling plan. Repetitive group sampling plan, Tightened-Normal-Tightened plan, Conditional repetitive group sampling plan and Link sampling plan as attribute plans. Illustrations with explanations and tables are provided to facilitate easy selection of plan. Suitable suggestions are also provided for future research. 2.15: Summary In this section the operating procedure of the various plans which are used in this thesis are presented. Further a detailed operating procedure and designing aspects of RMSPs are also presented. These procedures alone are adopted in constructing the various plans developed in this thesis. 32